You should be able to export www.mysite.com/anothersite to a WXR file using Tools » Export in your WordPress backend — www.mysite.com/anothersite/wp-admin. Then you can go to www.mysite.com/wp-admin, remove the existing content (delete your existing posts / pages / etc — export them first if you want/need a backup) and then use Tools » Import to import the WXR file.
